<span>the answer is 2(19d+17)</span>
Answer:
(12, 3.2) would be the max amount of gas he could buy. (11.25, 3) for an even gallon amount.
Step-by-step explanation:
First of all, let's find the slope of line L. To find the slope of a line, you write it in the explitic form
, and consider the coefficient
. So, we have
![2x - 3y = 5 \iff 3y = 2x-5 \iff y = \dfrac{2}{3} x - \dfrac{5}{3}](https://tex.z-dn.net/?f=%202x%20-%203y%20%3D%205%20%5Ciff%203y%20%3D%202x-5%20%5Ciff%20y%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%20x%20-%20%5Cdfrac%7B5%7D%7B3%7D%20)
So, the slope of line L is 2/3.
Two lines are parallel if they have the same slope. So, line M has slope 2/3 as well, and we know that it passes through the point (3, -10).
When you are given the slope
and a point
of a line, its equation is given by
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=%20y-y_0%3Dm%28x-x_0%29%20)
So, if you plug your values, you have
![y+10 = \dfrac{2}{3}(x-3)](https://tex.z-dn.net/?f=%20y%2B10%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%28x-3%29%20)
which you can simplify into
![y+10 = \dfrac{2}{3}x-2](https://tex.z-dn.net/?f=%20y%2B10%20%3D%20%5Cdfrac%7B2%7D%7B3%7Dx-2%20)
![y = \dfrac{2}{3}x-12](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cdfrac%7B2%7D%7B3%7Dx-12%20)
Answer:
D
Step-by-step explanation: